Question

In a reaction \(P+Q \rightarrow R+S\), there is no change in entropy. Enthalpy change for the reaction \((\Delta H)\) is \(12 \mathrm{~kJ} \mathrm{~mol}^{-1}\). Under what conditions, reaction will have negative value of free energy change? (a) If \(\Delta H\) is positive. (b) If \(\Delta H\) is negative. (c) If \(\Delta H\) is \(24 \mathrm{~kJ} \mathrm{~mol}^{-1}\). (d) If temperature of reaction is high.

Short answer

The reaction will have a negative value of free energy change only if \(\Delta H\) is negative, as in option (b).

Step-by-step solution

Understanding the Gibbs Free Energy Equation

To determine when the reaction will have a negative value of free energy change, we need to use the Gibbs free energy equation: \(\Delta G = \Delta H - T\Delta S\). Since we are given that there is no change in entropy (\(\Delta S = 0\)), the equation simplifies to \(\Delta G = \Delta H\) because \(T\Delta S\) will be zero.

Evaluating Option (a) - Positive \(\Delta H\)

If the enthalpy change \(\Delta H\) is positive, it means that \(\Delta G\) will also be positive, since \(\Delta G = \Delta H\) when \(\Delta S\) is zero. Therefore, the reaction will not have a negative value of free energy change under this condition.

Evaluating Option (b) - Negative \(\Delta H\)

If the enthalpy change \(\Delta H\) is negative, then \(\Delta G\), which equals \(\Delta H\), will also be negative. This means that the reaction will have a negative value of free energy change when \(\Delta H\) is negative.

Evaluating Option (c) - Specific Value of \(\Delta H\)

If the enthalpy change \(\Delta H\) is given a specific value, such as \(24 \mathrm{~kJ} \mathrm{~mol}^{-1}\), the value of \(\Delta G\) will be equal to the value of \(\Delta H\), which is positive. Hence, \(\Delta G\) would not be negative.

Evaluating Option (d) - High Temperature

High temperature affects the term \(T\Delta S\) in the Gibbs free energy equation. However, since \(\Delta S\) is zero, changes in temperature will not affect the value of \(\Delta G\). Therefore, simply increasing the temperature will not ensure a negative \(\Delta G\).

Key concepts

Understanding Thermodynamics

Thermodynamics is the branch of physics that deals with heat, work, and temperature, and their relation to energy, radiation, and physical properties of matter. It is a key concept when studying the spontaneous nature of chemical reactions and the energy changes that occur during these reactions.

At its heart is the idea that energy cannot be created or destroyed; it can only be transferred or changed from one form to another. This concept is known as the first law of thermodynamics or the law of conservation of energy. Understanding thermodynamics allows chemists to predict whether a chemical reaction will occur spontaneously and the theoretical yield of energy that can be obtained from the reaction.

Enthalpy Change Explained

Enthalpy change, denoted by \( \Delta H \) , is a measure of the total heat content in a thermodynamic system under constant pressure. It is a crucial part of understanding chemical reactions because it helps determine whether a reaction is endothermic (absorbs heat) or exothermic (releases heat).

An essential takeaway is that a negative \( \Delta H \) suggests that a reaction releases energy to its surroundings, typically heat, indicating it is exothermic. On the other hand, a positive \( \Delta H \) means the reaction absorbs energy, which means it is endothermic. In the context of the exercise, a negative \( \Delta H \) is necessary for the Gibbs free energy change, \( \Delta G \) , to be negative when entropy change is zero, thus driving the reaction forward.

Entropy and its Role in Reactions

Entropy, symbolized as \( \Delta S \) , describes the degree of disorder or randomness in a system. In chemical terms, it’s a quantitative measure of the amount of thermal energy in a system that is not available to do work. The second law of thermodynamics states that the total entropy of an isolated system can never decrease over time and is central in determining the direction of a chemical reaction.

A system will tend toward higher entropy, meaning natural processes prefer a state of increased randomness. In our exercise scenario, the reaction has no change in entropy; however, in general, if entropy increases during a reaction, it could contribute to a negative \( \Delta G \) and support a spontaneous reaction.

Chemical Reactions and Free Energy

A chemical reaction is a process where reactants are transformed into products. The feasibility of a chemical reaction under certain conditions can be estimated using the Gibbs free energy concept, \( \Delta G \). A negative value for \( \Delta G \) indicates that a reaction is spontaneous, while a positive value suggests that the reaction is non-spontaneous under those conditions.

The relationship between enthalpy, entropy, and temperature for predicting the spontaneity of a reaction is given by the Gibbs free energy equation. As we saw in the exercise, in the absence of entropy change, the sign of \( \Delta G \) solely depends on the sign of the enthalpy change, \( \Delta H \). Therefore, only when \( \Delta H \) is negative will the reaction potentially occur spontaneously, given that it’s the only term affecting \( \Delta G \) in such a scenario.